Extending on our newly introduced method to quantify the difference between two planetary system architectures, we also propose a method to compare between sets and catalogues of planetary systems, based on WED. We call this extension: ICED (Inter-Catalogue Energy Distance). Such a method can be useful in the context of forward models for population synthesis of planetary systems, such as SysSim [1]}, EPOS [2]} or NGPPS [3]}, [4]}. Quantifying the similarity of catalogues or simulated sets of planetary systems is usually done [2]}, [1]}, [3]}, [8]} by the Kolmogorov-Smirnov test statistic [9]}, [10]} and Anderson-Darling test statistic [11]} to compare between the distributions of planet properties, and with a Pearson \(\chi ^2\)  test or Cressie-Read power divergence [12]} to compare the distribution of planet multiplicity number [2]}, [1]}. We propose in this work to use ICED as a tool to quantify the similarity between two catalogues of planetary systems.
